Convexity of minimal total dominating functions of graphs

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dc.contributor.authorYu, Boen_US
dc.date.accessioned2024-08-15T20:19:58Z
dc.date.available2024-08-15T20:19:58Z
dc.date.copyright1992en_US
dc.date.issued1992
dc.degree.departmentDepartment of Mathematicsen_US
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractA total dominating function (TDF) of a graph is a function from its vertex set to the unit interval such that the sum of function values, taken over the open neighbourhood of each vertex, is at least one. T he thesis studies some basic properties of minimal total dominating functions (MTDFs) of graphs and in particular the question of when convex combinations of MTDFs are themselves MTDFs, especially on trees. We give a necessary and sufficient condition for graphs to have a unique MTDF and various conditions for genĀ­eral graphs and trees to have a universal MTDF. We characterize universal MTDFs of a certain class of trees. Several classes of trees with a universal MTDF or without a universal MTDF are given.
dc.format.extent73 pages
dc.identifier.urihttps://hdl.handle.net/1828/20247
dc.rightsAvailable to the World Wide Weben_US
dc.titleConvexity of minimal total dominating functions of graphsen_US
dc.typeThesisen_US

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